#1**+5 **

Hi 315 :)

Let K be the average number of Kilometres per year

Let C be the **yearly** compensation

The first one,

C1 = 0.223K+2000

when k=18000 C1= 0.223*18000+200 = 4214

The second one,

C2 = 0.32K

When K=18000 C2=0.32*18000 = 5760

**So at 18,000 km per year the second one gives the better compensation**

The reimbursements will be the same when C1=C2

0.223K+2000=0.32K

2000= (0.32-0.223)K

2000/(0.32-0.223) = 20618.5567010309278350515463917525773195876288659793814432989691

the reimburements will be the same if the annual distance travelled is 20619 km

Here is the graph :)

Melody Jun 18, 2016

#3**+5 **

Thank you Melody

I got it.

But there is a mistake in the first part Willie will receive 2000 not 200

thats why the total allowance of the first one is 6194 So the first one gives the better compensation.

but I totaly got the idea.

xvxvxv Jun 18, 2016

#5**0 **

For this question, I didn't get only this part

This area will require an average increase in a round-trip haul of 5 miles for 60% of the city.

What did he mean !

xvxvxv Jun 18, 2016

#7**0 **

Area is a confusing word.

It means the region of the tipping site.

Is the wording still confusing??

Melody Jun 18, 2016

#10**+5 **

Hi again 315. :)

Say the average round distance for Haul A is X miles

Then the average round distance for Haul B will be

60%*(x+5) + 20%*(X-2) +20%*X

=0.6X + 0.6*5 -0.2X - 0.2*2 +0.2X

= X + 0.6*5 - 0.2*2

This question is only concerned with the difference in the average distance so which is

=0.6*5 - 0.2*2

= 3 - 0.4

= 2.6 miles The average truck will travel 2.6miles further per load for plan B

Now I think that there are too many things that are poorly worded or not explained in this question BUT

this is my take.

What is the extra cost for part A.

I have to assume that the $2.35 / m^3 includes transport and material costs.

2.35*2*10^6 = 4.7*10^5 = 4.7 million dollars

**Extra costs for area A is 4.7 million dollars**

Now what are the extra costs for part B

Q how many truck loads will it take to fill the 14*10^6 m^3 tip

A 14*10^6 divided by 20 = 7*10^5 loads

Q and how many extra distance will this be for B?

A 2.6*7*10^5 = 1.82*10^6 miles

Q At 15mph how much extra time will this take?

A 1.82*10^6 divided by 15 = 121333 and 1/3 hours

Q At $35 pr hour how much extra cost will this be?

A 121333 and 1/3 hours *35 = $ 4246666.67

**Extra Cost for area B is 4.245 million dollars**

**Extra costs for area A is 4.7 million dollars**

**So, based on the information given, area B is cheaper.**

Melody
Jun 19, 2016

#8**+5 **

The first part concerning the auto dealer is irrelevant since he receives the same deal no matter which of his employer's plans he opts for.

a) At 18000 km per year, he receives 18000(.223) + 2000 = 6014 under the first option

Under the second option, he receives 18000(.32) = 5760 ......so the first option is better

b) Let x be the distance at which the reimbursements are the same....and we have....

.223(x) + 2000 = (.32)x rearrange as

2000 = 0.097x divide both sides by 0.097

x = about 20619 km

CPhill Jun 18, 2016